What is the Greatest Common Factor of 75105 and 75114?

Greatest common factor (GCF) of 75105 and 75114 is 9.

GCF(75105,75114) = 9

We will now calculate the prime factors of 75105 and 75114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75105 and 75114.

How to find the GCF of 75105 and 75114?

We will first find the prime factorization of 75105 and 75114. After we will calculate the factors of 75105 and 75114 and find the biggest common factor number .

Step-1: Prime Factorization of 75105

Prime factors of 75105 are 3, 5, 1669. Prime factorization of 75105 in exponential form is:

75105 = 3² × 5¹ × 1669¹

Step-2: Prime Factorization of 75114

Prime factors of 75114 are 2, 3, 13, 107. Prime factorization of 75114 in exponential form is:

75114 = 2¹ × 3³ × 13¹ × 107¹

Step-3: Factors of 75105

List of positive integer factors of 75105 that divides 75105 without a remainder.

1, 3, 5, 9, 15, 45, 1669, 5007, 8345, 15021, 25035

Step-4: Factors of 75114

List of positive integer factors of 75114 that divides 75105 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 107, 117, 214, 234, 321, 351, 642, 702, 963, 1391, 1926, 2782, 2889, 4173, 5778, 8346, 12519, 25038, 37557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75105 and 75114. The biggest common factor number is the GCF number.
So the greatest common factor 75105 and 75114 is 9.

Also check out the Least Common Multiple of 75105 and 75114